Details

sample121.0ms

Algorithm

intervals

Results

50.0ms	109×	body	1280	valid
17.0ms	52×	body	640	valid
8.0ms	155×	body	80	valid
8.0ms	37×	body	320	valid
6.0ms	158×	body	80	nan
5.0ms	5×	body	1280	nan
4.0ms	69×	body	80	overflowed
3.0ms	6×	body	640	nan
2.0ms	7×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	5×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 120

Calls

2 calls:

52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series417.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify64.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	542	2011
1	1694	1489
2	5001	1488

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 23.1b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
34×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
0.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow (+ x 1.0) (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
804.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	532	990
1	1951	912
2	5002	910

prune560.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 22.9b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
2.7b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
25×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`unpow-prod-down`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`pow1/3` `fma-udef`

Counts

4 → 83

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
1.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
0.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow (+ x 1.0) (/ 1.0 n))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
157.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.7s	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	685	1182
1	2511	1086
2	5002	1082

prune705.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.9b

localize45.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.8b	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.8b	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
2.7b	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (* (cbrt (* (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))))) (cbrt (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
0.0ms	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (* (cbrt (* (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))))) (cbrt (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
160.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
161.0ms	(cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))
1.7s	(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (* (cbrt (* (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))) (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n))))))) (cbrt (cbrt (fma 1.0 (/ 1 (* x n)) (- 1 (* 1.0 (/ (log (/ 1 x)) n)))))))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	543	1588
1	1961	1416
2	5001	1396

prune545.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.9b

regimes389.0ms

Accuracy

78.9% (1.8b remaining)

Error of 22.3b against oracle of 20.5b and baseline of 29.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	55
1	61	55
2	61	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	3140×	body	1280	valid
523.0ms	1501×	body	640	valid
254.0ms	4669×	body	80	valid
199.0ms	891×	body	320	valid
190.0ms	5033×	body	80	nan
160.0ms	171×	body	1280	nan
136.0ms	2291×	body	80	overflowed
111.0ms	232×	body	640	nan
63.0ms	457×	body	160	valid
40.0ms	156×	body	320	nan
11.0ms	87×	body	160	nan